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This paper provides some empirical estimates on how tightly is it feasible to control inflation in a very small open economy such as Iceland. Estimated macroeconomic models of Canada, Iceland, New Zealand, the United Kingdom, and the United States are used to derive efficient monetary policy frontiers that trace out the locus of the lowest combinations of inflation and output variability that are achievable under a range of alternative monetary policy rules. These frontiers illustrate that inflation stabilization is more challenging in Iceland than in other industrial countries primarily because of the relative magnitudes of the economic shocks.